I had the same issue on a fresh install of Archlinux.
I have never worked with ansible before so pardon if I make any bad reasoning but my issue was solved.

[root@netbootxyz netboot.xyz]# ansible-playbook -i inventory site.yml

gives the same error for me

The error message says it's coming from line 6 of generate_disks_base.yml shown here

[root@netbootxyz netboot.xyz]# cat roles/netbootxyz/tasks/generate_disks_base.yml

---

- name: Gathering facts
  ansible.builtin.setup:

- name: Gather variables for each operating system
  ansible.builtin.include_vars: "{{ item }}"
  with_first_found:
    - "{{ ansible_distribution | lower }}-{{ ansible_distribution_version | lower }}.yml"
    - "{{ ansible_distribution | lower }}-{{ ansible_distribution_major_version | lower }}.yml"
    - "{{ ansible_os_family | lower }}-{{ ansible_distribution_major_version | lower }}.yml"
    - "{{ ansible_distribution | lower }}.yml"
    - "{{ ansible_os_family | lower }}.yml"

The file names it is trying to find are generated from ansible.builtin.setup with the previous gathered facts step. On my system you can see one of those values here.

[root@netbootxyz netboot.xyz]# ansible localhost -m ansible.builtin.setup | grep ansible_os_family

[WARNING]: No inventory was parsed, only implicit localhost is available
        "ansible_os_family": "Archlinux",

So if it's looking for a file named "ansible_os_family | lower" would reduce to "archlinux.yml", but in what path?

[root@netbootxyz netboot.xyz]# find . -type f -name "*.yml"

 . . .
./user_overrides.yml
./script/netbootxyz-overrides.yml
./roles/netbootxyz/vars/ubuntu.yml
./roles/netbootxyz/vars/debian.yml
./roles/netbootxyz/vars/redhat.yml
./roles/netbootxyz/vars/main.yml

I see some os families have their own ansible files, but not archlinux. They seem responsible for installing packages in apt and pip, so I created a similar file that was empty with the understanding I might have to do some manual installs later.

.roles/netbootxyz/vars/archlinux.yml

---
netbootxyz_packages: []

pipxe_packages: []

After creating this file and running the following command, it appears to work and NBPs are generated.

[root@netbootxyz netboot.xyz]# ansible-playbook -i inventory site.yml

PLAY RECAP ********************************************************************************************************************************
localhost                  : ok=40   changed=16   unreachable=0    failed=0    skipped=22   rescued=0    ignored=0

I do not know what a more robust archlinux.yml file should contain to support self hosting netbootxyz the stub I created was sufficient. The only packages I installed manually were ansible, apache, and git.